A110269 -id:A110269 - cp's OEIS frontend

A238280 Irregular triangle read by rows, T(n,k) = Sum_{i = 1..n} k mod i, k = 1..m where m = lcm(1..n).

0, 1, 0, 2, 2, 1, 1, 3, 0, 3, 4, 4, 1, 4, 2, 5, 2, 2, 3, 6, 0, 4, 6, 7, 5, 4, 3, 7, 5, 6, 3, 7, 2, 6, 8, 4, 2, 6, 5, 9, 2, 3, 5, 9, 4, 3, 5, 6, 4, 8, 2, 6, 4, 5, 7, 6, 1, 5, 7, 8, 1, 5, 4, 8, 6, 2, 4, 8, 3, 7, 4, 5, 3, 7, 6, 5, 3, 4, 6, 10, 0, 5, 8, 10, 9, 9, 3, 8, 7, 9, 7, 12, 2, 7, 10, 7, 6, 11, 5, 10, 4, 6, 9, 14, 4, 4, 7, 9, 8, 13, 2, 7, 6, 8, 11

Offset: 1

Kival Ngaokrajang, Feb 22 2014

Row n contains A003418(n) terms.

The penultimate term (the one before zero) of row n = A000217(n-1).

			Row n of this irregular triangle is obtained by taking the first A003418(n) = lcm(1..n) terms (up to and including the first zero) of the following array (which starts at row n=1 and column k=1 and is periodic in each row):
  0; 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
  1  0; 1  0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1  0
  2  2  1  1  3  0; 2  2  1  1  3  0  2  2  1  1  3  0  2  2 # A110269
  3  4  4  1  4  2  5  2  2  3  6  0; 3  4  4  1  4  2  5  2
  4  6  7  5  4  3  7  5  6  3  7  2  6  8  4  2  6  5  9  2
  5  8 10  9  9  3  8  7  9  7 12  2  7 10  7  6 11  5 10  4
  6 10 13 13 14  9  8  8 11 10 16  7 13 10  8  8 14  9 15 10
  7 12 16 17 19 15 15  8 12 12 19 11 18 16 15  8 15 11 18 14
  8 14 19 21 24 21 22 16 12 13 21 14 22 21 21 15 23 11 19 16
  9 16 22 25 29 27 29 24 21 13 22 16 25 25 26 21 30 19 28 16

Antti Karttunen, Rows 1..10 of the table, flattened
Kival Ngaokrajang, Illustration for n = 1..10

Cf. A000217, A003418, A173185, A236856, A236857, A236858.

(define (A238280 n) (A238280tabf (A236857 n) (A236858 n)))
(define (A238280tabf n k) (add (lambda (i) (modulo k i)) 1 n))
;; Implements sum_{i=lowlim..uplim} intfun(i):
(define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (1+ i) (+ res (intfun i)))))))
;; Antti Karttunen, Feb 27 2014

A110270 a(n) = (n mod 2)*(n mod 3).

Original entry on oeis.org

0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 1, 0

Offset: 0

Reinhard Zumkeller, Jul 18 2005

Period 6: repeat [0, 1, 0, 0, 0, 2]. - Joerg Arndt, Aug 17 2014

Least positive integer k such that n^k == 1 (mod 6), or 0 if GCD(n,6) > 1. - Bruno Berselli, Mar 22 2016

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1).

Cf. A000035, A010872, A110269.

&cat [[0,1,0,0,0,2]^^20]; // Bruno Berselli, Mar 22 2016

A110270:=n->(n mod 2)*(n mod 3): seq(A110270(n), n=0..100); # Wesley Ivan Hurt, Aug 16 2014

Table[Mod[n,2]Mod[n,3],{n,0,110}] (* or *) PadRight[{},110,{0,1,0,0,0,2}] (* Harvey P. Dale, Oct 01 2013 *)

a(n) = (n % 2) * (n % 3); \\ Michel Marcus, Aug 17 2014

concat(0, Vec(x*(1+2*x^4)/((1-x)*(1+x)*(1-x+x^2)*(1+x+x^2)) + O(x^50))) \\ Colin Barker, Mar 22 2016

a(n) = A000035(n) * A010872(n).
a(n) = n mod (2 + n mod 2). - Wesley Ivan Hurt, Aug 16 2014
a(n) = a(n-6) for n>5. G.f.: x*(1+2*x^4) / ((1-x)*(1+x)*(1-x+x^2)*(1+x+x^2)). - Colin Barker, Mar 22 2016
a(n) = ( 6*sin(n*Pi/3) - sqrt(3) )*( sin(n*Pi/3) + sin(2*n*Pi/3) )/6. - Wesley Ivan Hurt, Jun 23 2016

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A238280 Irregular triangle read by rows, T(n,k) = Sum_{i = 1..n} k mod i, k = 1..m where m = lcm(1..n).

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A110270 a(n) = (n mod 2)*(n mod 3).

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